A351443 Odd numbers k for which A003958(sigma(k)) = A003958(k), where A003958 is multiplicative with a(p^e) = (p-1)^e and sigma is the sum of divisors function.

1, 49, 40905, 106353, 140211, 275301, 302697, 499041, 597213, 1094913, 1284417, 1578933, 2004345, 2266137, 2560653, 3247857, 3444201, 3738717, 4425921, 5014953, 5123817, 5211297, 5407641, 5505813, 5996673, 6193017, 6870339, 7174737, 8156457, 8941833, 9432693, 9825381, 9923553

Offset: 1

Author

Antti Karttunen, Feb 12 2022

Keywords

• nonn

Comments

Odd numbers k for which A351442(k) = A003958(k), or equally, for which k = A351444(k) = A322582(k) + A351442(k).

The 13th term, 2004345, is one of the rare abundant numbers (A005101, A005231) in this sequence.

Links

• Index entries for sequences where odd perfect numbers must occur, if they exist at all
• Index entries for sequences related to sigma(n)

Crossrefs

Odd terms in A351446.

Cf. A000203, A003958, A005101, A005231, A322582, A351442, A351444, A351445.

These terms doubled form a subsequence of A351447.

Programs

PARI

A003958(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]--); factorback(f); };
A351442(n) = A003958(sigma(n));
isA351443(n) = ((n%2) && (A351442(n)==A003958(n)));